As a fast-growing food production industry, aquaculture is dealing with the need for intensification due to the global increasing demand for fish products. However, this also implies the use of more sustainable practices to reduce negative environmental impacts currently associated with this industry, including the use of wild resources, destruction of natural ecosystems, eutrophication of effluent receiving bodies, impacts due to inadequate medication practices, among others. Using multi-species systems, such as integrated multi-trophic aquaculture, allows to produce economically important species while reducing some of these aquaculture concerns, through biomitigation of aquaculture wastes and reduction of diseases outbreaks, for example. Applying mathematical models to these systems is crucial to control and understand the interactions between species, maximizing productivity, with important environmental and economic benefits. Here, the application of some equations and models available in the literature, regarding basic parameters, is discussed – population dynamics, growth, waste production, and filtering rate – when considering the description and optimization of a theoretical integrated multi-trophic aquaculture operation composed by three trophic levels.